Two network cards

i. I have a Windows 2000 Pro workstation that has two network cards installed. One is connected to a network that has Internet access (via DSL). The other card is connected to a network that doesn’t have internet access (peer-to-peer).
When both network cards are enabled on my computer, I cannot access the internet. But when I disable the non-internet network card, I have internet access. Each card is configured to a static ip address, and each one connects perfectly. The problem is when both are enabled at the same time, internet access is broken.

Any help is greatly appreciated.